A thermomechanical constitutive model for phase transformations in silicon under pressure and contact loading conditions

Most of the technologically relevant abrasive machining techniques for silicon (Si) such as lapping, sawing and grinding are based on the interaction of the silicon surface with a hard particle or asperity. It has been long established that the governing deformation mechanism for Si under such contact loading conditions is stress induced phase transformation. The present work introduces a novel phenomenological constitutive model for phase transformations of silicon set up in a thermomechanical framework of broad applicability. Taking into account experimental observations as well as first principle and molecular dynamics calculations, it captures both the cd-Si → β-Si transition upon compression and the β-Si → a-Si transition upon rapid decompression, which are most relevant for indenter loading. The model was numerically implemented in analogy to incremental plasticity and successfully applied for finite-element (FE) simulations of nanoindentation.     

Investigation of the effect of pressure on some physical parameters and thermoelastic phase transformation of NiAl alloy

The Ni–Al alloys which exhibit the thermoelastic phase transformations in the composition range from 60 to 65 atomic percentage of Ni are widely used in the high technology applications. In this study, thermoelastic phase transformations of Ni–37.5 at.% Al alloys at 0, 1 and 2 GPa pressures were investigated by using MD simulation. Physical interactions among atoms in the alloy system were modelled using Sutton–Chen version of the embedded atom method based on many-body interactions. The potential parameters for cross interactions between Ni and Al atoms were estimated by optimising the results obtained from the molecular dynamics simulations. Moreover, the effect of applied pressure on transformation temperatures, enthalpy, entropy and elastic energy of model alloy system were investigated. The obtained result showed that the transformation temperature increased with applied pressure while enthalpy, entropy and elastic energy decreased. The values of the thermodynamical parameters that obtained in this study are in very good agreement with results of experimental studies.     

New investigations on transformation induced plasticity and its interaction with classical plasticity

In this paper, transformation induced plasticity (TRIP) in anisothermal single as well as double transformations (austenite → bainite and austenite → bainite + Martensite) in 16MND5 steel is experimentally analyzed. Several investigations have been performed related mainly on: (a) the evaluation of the physical mechanism responsible of the TRIP in bainitic transformation; (b) the kinetics of TRIP and its specificity in a double transformation; (c) the consequence when the load is applied during only a part of phase transformation; (d) the interaction between TRIP and classical plasticity and so on. The results seem indicate that Greenwood and Johnson mechanism is dominant compared to Magee mechanism. The interaction between classical plasticity and TRIP is clearly demonstrated and it seems that the strain hardening state of the parent phase plays an important role in the TRIP progress. Due to such interaction, TRIP appears even in the absence of external applied load; the behavior depends strongly on the transformation under consideration (bainitic or martensitic). From a modeling point of view, it is shown that Leblond’s model that is the only one “industrial” model which enables qualitatively to account for such interactions, fails to predict the observed phenomena especially in martensitic transformation.     

Buckling behavior of Kelvin open-cell foams under [0 0 1], [0 1 1] and [1 1 1] compressive loads

This paper describes buckling modes and stresses of elastic Kelvin open-cell foams subjected to [0 0 1], [0 1 1] and [1 1 1] uniaxial compressions. Cubic unit cells and cell aggregates in model foams are analyzed using a homogenization theory of the updated Lagrangian type. The analysis is performed on the assumption that the struts in foams have a non-uniform distribution of cross-sectional areas as observed experimentally. The relative density is changed to range from 0.005 to 0.05. It is thus found that long wavelength buckling and macroscopic instability primarily occur under [0 0 1] and [0 1 1] compressions, with only short wavelength buckling under [1 1 1] compression. The primary buckling stresses under the three compressions are fairly close to one another and almost satisfy the Gibson–Ashby relation established to fit experiments. By also performing the analysis based on the uniformity of strut cross-sectional areas, it is shown that the non-uniformity of cross-sectional areas is an important factor for the buckling behavior of open-cell foams.     

The high strain mechanical response of the wet Kelvin model for open-cell foams

Surface Evolver software was used to create the three-dimensional geometry of a Kelvin open-cell foam, to simulate that of polyurethane flexible foams. Finite Element Analysis (FEA) with 3D elements was used to model large compressive deformation in the [0 0 1] and [1 1 1] directions, using cyclic boundary conditions when necessary, treating the polyurethane as an elastic or elastic–plastic material. The predicted foam Young’s moduli in the [0 0 1] direction are double those of foams with uniform Plateau border cross-section edges, for the same foam density and material properties. For compression in the [1 1 1] direction, the normalized Young’s modulus increases from 0.9 to 1.1 with foam relative density, and the predicted stress–strain relationship can have a plateau, even for a linearly-elastic polymer. As the foam density increases, the predicted effects of material plasticity become larger. For foam of relative density 0.028, edge-to-edge contact is predicted to occur at a 66% strain for [1 1 1] direction compression. The foam is predicted to contract laterally when the [1 1 1] direction compressive strain exceeds 25%.     

Superelastic shape memory alloy cables: Part II – Subcomponent isothermal responses

This paper constitutes the second part of our experimental study of the thermo-mechanical behavior of superelastic NiTi shape memory alloy cables. Part I introduced the fundamental, room temperature, tensile responses of two cable designs (7 × 7 right regular lay, and 1 × 27 alternating lay). In Part II, each cable behavior is studied further by breaking down the response into the contributions of its hierarchical subcomponents. Selected wire strands were extracted from the two cable constructions, and their quasi-static tension responses were measured using the same experimental setup of Part I. Consistent with the shallow wire helix angles in the 7 × 7 construction, the force–elongation responses of the core wire, 1 × 7 core strand and full 7 × 7 cable were similar on a normalized basis, with only a slight decrease in transformation force plateaus and slight increase in plateau strains in this specimen sequence. By contrast, each successive 1 × 27 component (1 × 6 core strand, 1 × 15 strand, and full cable) included an additional outer layer of wires with a larger number of wires, greater helix radius, and deeper helix angle, so the normalized axial load responses became significantly more compliant. Each specimen in the sequence also exhibited progressively larger strains at failure, reaching 40% strain in the full 1 × 27 cable.Stress-induced phase transformations involved localized strain/temperature and front propagation in all of the tested 7 × 7 components but none of the 1 × 27 components aside from the 1 × 27 core wire. Stereo digital image correlation measurements revealed finer features within a global transformation front of the 1 × 7 core strand than the 7 × 7 cable, consisting of an staggered pattern of individual wire fronts that moved in lock-step during elongation. Although the 1 × 27 multi-layer strands exhibited temperature/strain localizations in a distributed pattern during transformations, the localizations did not propagate and their cause was traced back to contact indentations (stress concentrations) arising from the cable’s fabrication. The normalized axial torque responses of the multi-layer 1 × 27 components during transformation were distinctly non-monotonic and complex, due to the alternating handedness of the layers. Force and torque contributions of individual wire layers were deduced by subtracting 1 × 27 component responses, which helped to clarify the transformation kinetics within each layer and explain the unusual force and torque undulations seen in the 1 × 27 cable response of Part I.     

Particle deposition model for particulate flows at high temperatures in gas turbine components

This study proposes an improved physical model to predict sand deposition at high temperature in gas turbine components. This model differs from its predecessor (Sreedharan and Tafti, 2011) by improving the sticking probability by accounting for the energy losses during particle-wall collision based on our previous work (Singh and Tafti, 2013). This model predicts the probability of sticking based on the critical viscosity approach and collision losses during a particle–wall collision. The current model is novel in the sense that it predicts the sticking probability based on the impact velocity along with the particle temperature. To test the model, deposition from a sand particle laden jet impacting on a flat coupon geometry is computed and the results obtained from the numerical model are compared with experiments (Delimont et al., 2014) conducted at Virginia Tech, on a similar geometry and flow conditions, for jet temperatures of 950 °C, 1000 °C and 1050 °C. Large Eddy Simulations (LES) are used to model the flow field and heat transfer, and sand particles are modeled using a discrete Lagrangian framework. Results quantify the impingement and deposition for 20–40 μm sand particles. The stagnation region of the target coupon is found to experience most of the impingement and deposition. For 950 °C jet temperature, around 5% of the particle impacting the coupon deposit while the deposition for 1000 °C and 1050 °C is 17% and 28%, respectively. In general, the sticking efficiencies calculated from the model show good agreement with the experiments for the temperature range considered.     

An investigation of a model of the flow pattern transition mechanism in relation to the identification of annular flow of R134a in a vertical tube using various void fraction models and flow regime maps

In the present study, new experimental data are presented for literature on the prediction of film thickness and identification of flow regime during the co-current downward condensation in a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm. R134a and water are used as working fluids in the tube side and annular side of a double tube heat exchanger, respectively. Condensation experiments are done at mass fluxes of 300 and 515 kg m^?2 s^?1. The condensing temperatures are between 40 and 50 °C; heat fluxes are between 12.65 and 66.61 kW m^?2. The average experimental heat transfer coefficient of the refrigerant HFC-134a is calculated by applying an energy balance based on the energy transferred from the test section. A mathematical model by Barnea et al. based on the momentum balance of liquid and vapor phases is used to determine the condensation film thickness of R134a. The comparative film thickness values are determined indirectly using relevant measured data together with various void fraction models and correlations reported in the open literature. The effects of heat flux, mass flux, and condensation temperature on the film thickness and condensation heat transfer coefficient are also discussed for the laminar and turbulent flow conditions. There is a good agreement between the film thickness results obtained from the theoretical model and those obtained from six of 35 void fraction models in the high mass flux region of R134a. In spite of their different valid conditions, six well-known flow regime maps from the literature are found to be predictive for the annular flow conditions in the test tube in spite of their different operating conditions.     

In-plane free vibration of a single-crystal silicon ring

In this paper the natural frequencies and the associated mode shapes of in-plane free vibration of a single-crystal silicon ring are analyzed. It is found that the Si(1 1 1) ring is two-dimensionally isotropic in the (1 1 1) plane for elastic constants but three-dimensionally anisotropic, while the Si(1 0 0) ring is fully anisotropic. Hamilton’s principle is used to derive the equations of vibration, which is a set of partial differential equations with coefficients being periodic in polar variable. Expressing the radial and tangential displacements in sinusoidal form with non-predetermined amplitudes, and through the integration with respect to the circumferential variable, the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form. The exact expressions for frequencies and mode shapes are obtained. It is found that for Si(1 0 0) rings the frequencies of a pair of modes, which are equal for an isotropic ring, split due to the anisotropic effect only for the second in-plane vibration mode. The phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups. When the single-crystal silicon is replaced by the polycrystalline silicon, which is isotropic in elastic constants, the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

Investigations of phase inversion and frictional pressure gradients in upward and downward oil–water flow in vertical pipes

The present study has attempted to investigate phase inversion and frictional pressure gradients during simultaneous vertical flow of oil and water two-phase through upward and downward pipes. The liquids selected were white oil (44 mPa s viscosity and 860 kg/m³ density) and water. The measurements were made for phase velocities varying from 0 to 1.24 m/s for water and from 0 to 1.87 m/s for oil, respectively. Experiments were carried either by keeping the mixture velocity constant and increasing the dispersed phase fraction or by keeping the continuous phase superficial velocity constant and increasing the dispersed phase superficial velocity. From the experimental results, it is shown that the frictional pressure gradient reaches to its lower value at the phase inversion point in this work. The points of phase inversion are always close to an input oil fraction of 0.8 for upward flow and of 0.75 for downward flow, respectively. A few models published in the literature are used to predict the phase inversion point and to compare the results with available experimental data. Suitable methods are suggested to predict the critical oil holdup at phase inversion based on the different viscosity ratio ranges. Furthermore, the frictional pressure gradient is analyzed with several suitable theoretical models according to the existing flow patterns. The analysis reveals that both the theoretical curves and the experimental data exhibit the same trend and the overall agreement of predicted values with experimental data is good, especially for a high oil fraction.     

CFD simulation of a gas–solid fluidized bed with two vertical jets

A computational fluid dynamics (CFD) model is used to investigate the hydrodynamics of a gas–solid fluidized bed with two vertical jets. Sand particles with a density of 2660 kg/m³ and a diameter of 5.0 × 10^?4 m are employed as the solid phase. Numerical computation is carried out in a 0.57 m × 1.00 m two-dimensional bed using a commercial CFD code, CFX 4.4, together with user-defined Fortran subroutines. The applicability of the CFD model is validated by predicting the bed pressure drop in a bubbling fluidized bed, and the jet detachment time and equivalent bubble diameter in a fluidized bed with a single jet. Subsequently, the model is used to explore the hydrodynamics of two vertical jets in a fluidized bed. The computational results reveal three flow patterns, isolated, merged and transitional jets, depending on the nozzle separation distance and jet gas velocity and influencing significantly the solid circulation pattern. The jet penetration depth is found to increase with increasing jet gas velocity, and can be predicted reasonably well by the correlations of Hong et al. (2003) for isolated jets and of Yang and Keairns (1979) for interacting jets.     

Periodic group crack problems in an infinite plate

This paper investigates periodic group crack problems in an infinite plate. The periodic group crack is composed of infinite groups with numbering from j = −∞, …, −2, −1, 0, 1, 2, …, to j = ∞, and the groups are placed periodically. The same loading condition and the same geometry are assumed for cracks in all groups. A singular integral equation is used to solve the problems. The singular integral equation is formulated on cracks of the 0th group (or the central group) with the collection of influences from the infinite groups. The influences of many neighboring groups to the central group are evaluated exactly. Meantime, the influences of many remote groups to the central group can be summed up into one term approximately. The stress intensity factors at crack tips can be evaluated from the solution of the singular integral equation. It is found from some sample problems that the obtained results are very accurate. Finally, several numerical examples are presented and interaction among the group cracks is addressed.     

Experimental investigation of turbulence modulation in particle-laden coaxial jets by Phase Doppler Anemometry

The effect of solid particles on the flow characteristics of axisymmetric turbulent coaxial jets for two flow conditions was studied. Simultaneous measurements of size and velocity distributions of continuous and dispersed phases in a two-phase flow are presented using a Phase Doppler Anemometry (PDA) technique. Spherical glass particles with a particle diameter range from 102 to 212 μm were used in this two-phase flow, the experimental results indicate a significant influence of the solid particles and the Re on the flow characteristics. The data show that the gas phase has lower mean velocity in the near-injector region and a higher mean velocity at the developed region. Near the injector at low Reynolds number (Re = 2839) the presence of the particles dampens the gas-phase turbulence, while at higher Reynolds number (Re = 11 893) the gas-phase turbulence and the velocity fluctuation of particle-laden jets are increased. The particle velocity at higher Reynolds number (Re = 11 893) and is lower at lower Reynolds number (Re = 2839). The slip velocity between particles and gas phase existed over the flow domain was examined. More importantly, the present experiment results suggest that, consideration of the gas characteristic length scales is insufficient to predict gas-phase turbulence modulation in gas-particle flows.     

Evaluation of subgrid-scale models in large-eddy simulation of flow past a two-dimensional block

Large-eddy simulations of flow past a two-dimensional (2D) block were performed to evaluate four subgrid-scale (SGS) models: (i) the traditional Smagorinsky model, (ii) the Lagrangian dynamic model, (iii) the Lagrangian scale-dependent dynamic model, and (iv) the modulated gradient model. An immersed boundary method was employed to simulate the 2D block boundaries on a uniform Cartesian grid. The sensitivity of the simulation results to grid refinement was investigated by using four different grid resolutions. The velocity streamlines and the vertical profiles of the mean velocities and variances were compared with experimental results. The modulated gradient model shows the best overall agreement with the experimental results among the four SGS models. In particular, the flow recirculation, the reattachment position and the vertical profiles are accurately reproduced with a relative coarse grid resolution of (N_x × N_y × N_z=) 160 × 40 × 160 (n_x × n_z = 13 × 16 covering the block). Besides the modulated gradient model, the Lagrangian scale-dependent dynamic model is also able to give reasonable prediction of the flow statistics with some discrepancies compared with the experimental results. Relatively poor performance by the Lagrangian dynamic model and the Smagorinsky model is observed, with simulated recirculating patterns that differ from the measured ones. Analysis of the turbulence kinetic energy (TKE) budget in this flow shows evidence of a strong production of TKE in the shear layer that forms as the flow is deflected around the block.     

CFD modelling and wind tunnel validation of airflow through plant canopies using 3D canopy architecture

The efficiency of pesticide application to agricultural fields and the resulting environmental contamination highly depend on atmospheric airflow. A computational fluid dynamics (CFD) modelling of airflow within plant canopies using 3D canopy architecture was developed to understand the effect of the canopy to airflow. The model average air velocity was validated using experimental results in a wind tunnel with two artificial model trees of 24 cm height. Mean air velocities and their root mean square (RMS) values were measured on a vertical plane upstream and downstream sides of the trees in the tunnel using 2D hotwire anemometer after imposing a uniform air velocity of 10 m s^?1 at the inlet. 3D virtual canopy geometries of the artificial trees were modelled and introduced into a computational fluid domain whereby airflow through the trees was simulated using Reynolds-Averaged Navier–Stokes (RANS) equations and k-ε turbulence model. There was good agreement of the average longitudinal velocity, U between the measurements and the simulation results with relative errors less than 2% for upstream and 8% for downstream sides of the trees. The accuracy of the model prediction for turbulence kinetic energy k and turbulence intensity I was acceptable within the tree height when using a roughness length (y₀ = 0.02 mm) for the surface roughness of the tree branches and by applying a source model in a porous sub-domain created around the trees. The approach was applied for full scale orchard trees in the atmospheric boundary layer (ABL) and was compared with previous approaches and works. The simulation in the ABL was made using two groups of full scale orchard trees; short (h = 3 m) with wider branching and long (h = 4 m) with narrow branching. This comparison showed good qualitative agreements on the vertical profiles of U with small local differences as expected due to the spatial disparities in tree architecture. This work was able to show airflow within and above the canopy in 3D in more details.     

Static wall layers in plane channel displacement flows

We study steady and pulsating displacement flows of a Bingham fluid by a Newtonian fluid, along a plane channel. For sufficiently large yield stress a static residual wall layer can result during the displacement. The flow is parameterised by the Reynolds number (Re), the Bingham number (B) and the viscosity ratio (M). Perhaps intuitively, thicker layers are found with larger M and at lower Re. The residual layer is formed on the advective timescale of the displacement but drains on a slower timescale governed by M. For larger M truly stationary layers are only found for large t when the layer has thinned sufficiently to become static. Increased Re results in increased energy production locally around the finger. For large enough Re the energy production can play a significant role in yielding the fluid. As the energy production rate increases it also becomes focused around the corner or shoulder region of the front, and spreads axially along the initial part of the residual layer. This causes fluid to yield increasingly far behind the front and allows for the layer to thin. As B increases the static layer tends to decrease (see also [1], [2]). At small Re the static layer thickness appears to be independent of M. At large Re the layer thickness is dependent on M and decreases asymptotically to a constant value as B → ∞.For pulsating displacement flow rates, Q(t) = 2(1 + Asin  ωt) : A ∈ [0, 1) we study two ranges: ωRe ? 2π and ωRe ? 2π. For the viscous regime (ωRe ? 2π) a pseudo-steady 1D model predicts that the residual layer should remain static for 3(1 + Asin  ωt) < MB. In practice we find that partial mobilisation of the residual layer occurs even when this inequality is satisfied, but not if MB becomes significantly larger than 3(1 + A). For ωRe ? 2π we mobilise the layer for significantly larger values of MB and at smaller A, than in the viscous regime. This effect is traced to the occurrence of out-of-phase velocity fluctuations in the displacing fluid within a wall layer close to the interface.     

Influence of single rectangular groove on the flow past a circular cylinder

In the present study, flow control mechanism of single groove on a circular cylinder surface is presented experimentally using Particle image velocimetry (PIV). A square shaped groove is patterned longitudinally on the surface of the cylinder with a diameter of 50 mm. The flow characteristics are studied as a function of angular position of the groove from the forward stagnation point of the cylinder within 0° ≤ θ ≤ 150°. In the current work, instantaneous and time-averaged flow data such as vorticity, ω streamline, Ψ streamwise, u/U_o and transverse, v/U_o velocity components, turbulent kinetic energy, TKE and RMS of streamwise, u_rms and transverse, v_rms velocity components are utilized in order to present the results of quantitative analyses. Furthermore, Strouhal numbers are calculated using Karman vortex shedding frequency, f_k obtained from single point spectral analysis. It is concluded that a critical angular position of the groove, θ = 80° is observed. The flow separation is controlled within 0° ≤ θ < 80°. At θ = 80°, the flow separation starts to occur in the upstream direction. The instability within the shear layer is also induced on grooved side of the cylinder with frequencies different than Karman vortex shedding frequency, f_k.     

Numerical analysis of turbulent convection heat transfer from an array of perforated fins

Numerical investigation is made for three-dimensional fluid flow and convective heat transfer from an array of solid and perforated fins that are mounted on a flat plate. Incompressible air as working fluid is modeled using Navier–Stokes equations and RNG based k ? ? turbulent model is used to predict turbulent flow parameters. Temperature field inside the fins is obtained by solving Fourier’s conduction equation. The conjugate differential equations for both solid and gas phase are solved simultaneously by finite volume procedure using SIMPLE algorithm. Perforations such as small channels with square cross section are arranged streamwise along the fin’s length and their numbers varied from 1 to 3. Flow and heat transfer characteristics are presented for Reynolds numbers from 2 × 10⁴ to 4 × 10⁴ based on the fin length and Prandtl number is taken Pr = 0.71. Numerical computations are validated with experimental studies of the previous investigators and good agreements were observed. Results show that fins with longitudinal pores, have remarkable heat transfer enhancement in addition to the considerable reduction in weight by comparison with solid fins.     

Argon K-shell and bound-free emission from OMEGA direct-drive implosion cores

We discuss calculations of synthetic spectra for the interpretation and analysis of K-shell and bound-free emission from argon-doped deuterium-filled OMEGA direct-drive implosion cores. The spectra are computed using a model that considers collisional-radiative atomic kinetics, continuum-lowering, detailed Stark-broadened line shapes, line overlapping, and radiation transport effects. The photon energy range covers the moderately optically thick n = 3 → n = 1 and n = 4 → n = 1 line transitions in He- and H-like Ar, their associated satellite lines in Li- and He-like Ar, and several radiative recombination edges. At the high-densities characteristic of implosion cores, the radiative recombination edges substantially shift to lower energies thus overlapping with several line transitions. We discuss the application of the spectra to spectroscopic analysis of doped implosion cores.